I have an 02 trailblazer, and had some oil leaking through the gaskets, there was air pressure when i opened the oil cap, when i have the truck stopped at a light, the oil pressure gauge goes all the way down and the messege tells me low oil pressure shut off engine. I had a hose cleaned that was restricting air flow also put a new valve cover gasket on but still having issues.

 

Have you checked the oil pressure switch? Just replaced mine, was doing the same as yours.